Class 9 Mathematics Chapter 6 Number Play: Complete Important Questions & Answers

The CBSE Board exam pattern for Class 9 emphasizes conceptual understanding over mechanical computation. Number Play questions test three critical skills: (1) application of integer properties to solve problems, (2) pattern recognition in sequences and algebraic expressions, and (3) real-world use of negative numbers in contexts like temperature, banking, and elevation. The 2024-25 rationalized syllabus has streamlined content to focus on meaningful problem-solving. Questions no longer test rote memorization but instead require you to justify why a + b = b + a (commutativity) or explain why a × (b + c) = ab + ac (distributivity). Board examiners increasingly ask: "Why does this property work?" and "How would you apply this to a new situation?" Roughly 8–12% of the Class 9 paper draws from Number Play. This includes 1-mark MCQs on property identification, 2-mark questions on integer word problems, and 3–5 mark questions requiring multi-step reasoning with negative numbers and patterns. Mastering these questions builds the integer sense needed for algebraic manipulation in higher grades.

**Question 1:** Which property of integers is demonstrated by the equation 7 + (–7) = 0? A) Commutative property B) Associative property C) Additive inverse property D) Distributive property **Answer:** C) Additive inverse property *Explanation:* When an integer and its negative are added, the sum is zero. This defines the additive inverse property. **Question 2:** If a = –5 and b = 3, then a × b is: A) –15 B) 15 C) 8 D) –8 **Answer:** A) –15 *Explanation:* Negative × Positive = Negative. So –5 × 3 = –15. **Question 3:** The next number in the pattern 2, 5, 10, 17, 26, ... is: A) 35 B) 37 C) 39 D) 41 **Answer:** B) 37 *Explanation:* Differences are 3, 5, 7, 9, 11. These are odd numbers increasing by 2. Next difference is 11, so 26 + 11 = 37. **Question 4:** Which statement about integer division is true? A) a ÷ b = b ÷ a for all integers a, b B) Division of integers is not closed (result may not be an integer) C) (a ÷ b) ÷ c = a ÷ (b ÷ c) always D) 0 ÷ a = a for any non-zero integer a **Answer:** B) Division of integers is not closed *Explanation:* For example, 7 ÷ 2 = 3.5, which is not an integer. Integers are not closed under division. **Question 5:** The temperature at sunrise was –8°C. By noon it rose by 15°C. What was the temperature at noon? A) 7°C B) –23°C C) 8°C D) 23°C **Answer:** A) 7°C *Explanation:* –8 + 15 = 7°C. Addition of integers in a real-world context.

**Question 1:** Verify that (–9) × (4 + 5) = (–9) × 4 + (–9) × 5. Which property does this demonstrate? **Solution:** Left side: (–9) × (4 + 5) = (–9) × 9 = –81 Right side: (–9) × 4 + (–9) × 5 = –36 + (–45) = –81 Both sides equal –81. ✓ *Property demonstrated:* Distributive property of multiplication over addition. **Question 2:** A diver descends 12 m below sea level. He then ascends 8 m. Write his current position relative to sea level using integers, and calculate the net change. **Solution:** Initial position: –12 m (below sea level) After ascending 8 m: –12 + 8 = –4 m Current position: 4 m below sea level (or –4 m relative to sea level) Net change: 8 m upward **Question 3:** If a = 3, b = –4, and c = 2, find the value of a + (b + c) and (a + b) + c. What property is verified? **Solution:** a + (b + c) = 3 + (–4 + 2) = 3 + (–2) = 1 (a + b) + c = (3 + (–4)) + 2 = (–1) + 2 = 1 Both equal 1. ✓ *Property verified:* Associative property of addition. **Question 4:** Write the first five terms of the pattern where the nth term is n² – n. Then find the 6th term. **Solution:** For n = 1: 1² – 1 = 0 For n = 2: 2² – 2 = 2 For n = 3: 3² – 3 = 6 For n = 4: 4² – 4 = 12 For n = 5: 5² – 5 = 20 First five terms: 0, 2, 6, 12, 20 For n = 6: 6² – 6 = 36 – 6 = 30 6th term: 30 **Question 5:** A bank account has a balance of –₹500 (overdrawn). After a deposit of ₹1200, what is the new balance? Express using integers and explain the operation. **Solution:** Initial balance: –₹500 Deposit (positive): +₹1200 New balance: –500 + 1200 = ₹700 The account now has a credit of ₹700.

**Question 1:** Prove that the set of integers is closed under addition and subtraction but not under division. Give one example for each case. **Solution:** *Closure under addition:* For any integers a and b, a + b is always an integer. Example: 5 + (–3) = 2 ✓ (integer) *Closure under subtraction:* For any integers a and b, a – b is always an integer. Example: –7 – 4 = –11 ✓ (integer) *Not closed under division:* For some integers a and b, a ÷ b is not an integer. Example: 5 ÷ 2 = 2.5 ✗ (not an integer) Therefore, integers are closed under addition and subtraction but not division. **Question 2:** A number pattern is defined as: First term = 5, and each subsequent term is obtained by multiplying the previous term by (–1) and adding 2. Write the first six terms and identify the pattern. **Solution:** Term 1: 5 Term 2: 5 × (–1) + 2 = –5 + 2 = –3 Term 3: (–3) × (–1) + 2 = 3 + 2 = 5 Term 4: 5 × (–1) + 2 = –3 Term 5: (–3) × (–1) + 2 = 5 Term 6: 5 × (–1) + 2 = –3 First six terms: 5, –3, 5, –3, 5, –3 *Pattern:* The sequence alternates between 5 and –3 with period 2. **Question 3:** Using the properties of integers, simplify: [–8 + (–12)] × 3 + 6 ÷ (–2). Show each step. **Solution:** Step 1: Simplify inside brackets: –8 + (–12) = –20 Step 2: Multiply: –20 × 3 = –60 Step 3: Divide: 6 ÷ (–2) = –3 Step 4: Add: –60 + (–3) = –63 Final answer: –63 **Question 4:** The sum of three consecutive integers is –12. Find the three integers. Verify your answer. **Solution:** Let the three consecutive integers be n, n+1, n+2. Sum: n + (n+1) + (n+2) = –12 3n + 3 = –12 3n = –15 n = –5 The three integers are: –5, –4, –3 *Verification:* –5 + (–4) + (–3) = –12 ✓

**Question 1:** A student's monthly savings record is represented as: Months 1–3 saw a loss of ₹200 per month. Months 4–6 saw a gain of ₹150 per month. Months 7–9 saw a loss of ₹100 per month. Calculate the net change and final balance if the initial balance was ₹5000. Explain your calculation using integer operations. **Solution:** *Loss in Months 1–3:* 3 × (–200) = –₹600 *Gain in Months 4–6:* 3 × 150 = ₹450 *Loss in Months 7–9:* 3 × (–100) = –₹300 *Net change:* –600 + 450 + (–300) = –600 + 450 – 300 = –450 *Final balance:* 5000 + (–450) = ₹4550 *Explanation:* We used the distributive property to group losses and gains, then applied integer addition to compute the net change. The final balance demonstrates practical application of negative and positive integers in financial contexts. **Question 2:** The general term of a sequence is defined as aₙ = (–1)ⁿ × n². Find the first eight terms, then calculate the sum of all eight terms. Explain the pattern in signs. **Solution:** For n = 1: a₁ = (–1)¹ × 1² = –1 For n = 2: a₂ = (–1)² × 2² = 4 For n = 3: a₃ = (–1)³ × 3² = –9 For n = 4: a₄ = (–1)⁴ × 4² = 16 For n = 5: a₅ = (–1)⁵ × 5² = –25 For n = 6: a₆ = (–1)⁶ × 6² = 36 For n = 7: a₇ = (–1)⁷ × 7² = –49 For n = 8: a₈ = (–1)⁸ × 8² = 64 *First eight terms:* –1, 4, –9, 16, –25, 36, –49, 64 *Sum:* (–1 + 4) + (–9 + 16) + (–25 + 36) + (–49 + 64) = 3 + 7 + 11 + 15 = 36 *Pattern explanation:* (–1)ⁿ alternates the sign—odd n give negative terms, even n give positive terms. Consecutive pairs sum to positive odd numbers: 3, 7, 11, 15 (arithmetic sequence with common difference 4). **Question 3:** Two friends play a number game. Friend A starts with 0 points. In each round, Friend A either gains 5 points (represented as +5) or loses 3 points (represented as –3). After 10 rounds with 6 gains and 4 losses, calculate the final score. Then, verify using the distributive property that 6(+5) + 4(–3) produces the same result as adding the individual operations in any order. **Solution:** *Direct calculation:* 6 × 5 + 4 × (–3) = 30 + (–12) = 30 – 12 = 18 *Final score:* 18 points *Verification using Distributive property:* Method 1 (gains first): (+5) + (+5) + (+5) + (+5) + (+5) + (+5) + (–3) + (–3) + (–3) + (–3) = 30 + (–12) = 18 Method 2 (mixed order): (+5) + (–3) + (+5) + (–3) + (+5) + (–3) + (+5) + (–3) + (+5) + (+5) Grouping: 4 × [(+5) + (–3)] + 2 × (+5) = 4 × 2 + 10 = 8 + 10 = 18 *Both methods yield 18 points, confirming commutativity and associativity of integer addition.*

**Case Study:** A climate research team tracks temperature anomalies (deviations from normal) across 5 consecutive days. The anomalies recorded are: Day 1 = –4°C, Day 2 = –2°C, Day 3 = +1°C, Day 4 = +3°C, Day 5 = +2°C. (a) Calculate the total anomaly over all 5 days. (b) If the team wants to represent this using a formula where aₙ = –4 + (n–1) × d, where n is the day number and d is the common difference, verify if the sequence follows an arithmetic pattern. (c) On Day 6, if the anomaly follows the same arithmetic pattern, what would it be? (d) Explain why understanding negative and positive number operations is critical for climate science. **Solution:** *(a) Total anomaly calculation:* Sum = (–4) + (–2) + (+1) + (+3) + (+2) Grouping negatives: (–4) + (–2) = –6 Grouping positives: 1 + 3 + 2 = 6 Total: –6 + 6 = 0°C The net temperature anomaly over 5 days is 0°C (returns to normal). *(b) Verify arithmetic pattern:* Day 1: –4°C (given) Day 2: –2°C (difference: –2 – (–4) = 2) Day 3: +1°C (difference: 1 – (–2) = 3) Day 4: +3°C (difference: 3 – 1 = 2) Day 5: +2°C (difference: 2 – 3 = –1) Differences: 2, 3, 2, –1 → Not constant. *Conclusion:* The sequence does NOT follow a simple arithmetic pattern. The formula aₙ = –4 + (n–1) × d with constant d does not apply. *(c) Day 6 prediction:* Since no consistent pattern exists using a single formula, we observe the trend: The anomaly increased from Day 1 to Day 4, then decreased. If we assume the sequence continues with some regularity or based on available data, Day 6 might show continued cooling or return toward normal. Without a definite pattern, Day 6 cannot be reliably predicted from the given data alone. *(d) Why this matters in climate science:* Climate scientists use negative and positive anomalies to represent cooling and warming relative to a baseline. Understanding integer operations allows them to: — Compute net changes (sum of anomalies) — Identify trends (consecutive increases/decreases) — Predict future values using patterns (arithmetic or geometric sequences) — Communicate deviations clearly (negative = cooler; positive = warmer) Mastery of these operations is foundational to interpreting climate models and real-world data.

Solving these 18 important questions once gives you a snapshot of your understanding. But genuine mastery requires repetition, immediate feedback, and personalized reinforcement. At CBSETUTOR.ai, our AI tutor mimics the exact questioning patterns you'll face on the Board exam—MCQ sequences, short-answer reasoning chains, and multi-step problem-solving. Every day, you receive a custom drill tailored to your weak areas. Attempt a 3-mark question on integer properties? Our AI instantly identifies if you've applied commutativity correctly or confused closure with identity. It then serves you 3–4 similar variations so the pattern sticks. Unlike textbooks, our AI adjusts difficulty in real time: if you ace 2-mark questions, it unlocks harder 3–5 mark scenarios. For Chapter 6, you'll drill integer operation applications (banking, temperature), number pattern recognition, and property-based reasoning until they become second nature. Parent-verified progress reports show exactly which topics need more focus. Start a 3-day free trial at cbsetutor.ai and see how daily AI-powered drills transform Chapter 6 from confusing to confident.